Phononic metamaterials enable the manipulation of both elastic and acoustic waves in different media, from attenuation (including absorption and reflection) to coupling, tunneling, negative refraction and focusing. In particular, the attenuation of vibrations, such as vector mechanical vibrations through a solid, or a scalar acoustic vibration in a medium, such as in air or water, is important technologically for applications where the presence of such vibrations affects the intended performance of the device or entity in question, such as, but not limited to, a vehicle. Another example of this is the attenuation of high frequency (>2 KHz) sound in acoustic hearing aids.
In general, acoustic materials can be categorized according to their effect upon sounds. A sound insulating material is an acoustic material which can intercept and reflect a sound wave which is propagating through a fluid medium such as air, as opposed to a solid material (in other words, an elastic wave). Sound insulators are typically materials which have a high surface density, for example bricks and concrete.
A sound absorbing material is typically an acoustic material which is porous such that an airborne sound wave can propagate into the material with the mechanical or vibrational energy of the sound wave being reduced by converting the energy into thermal energy due to friction within the material. Examples of sound absorbing materials include open cell foamed plastics, fiberglass, blankets and the like.
Likewise, vibration dampening materials are acoustic materials which can intercept a sound wave propagating through a solid material, as opposed to air. The mechanical or vibrational energy of the sound wave is reduced by converting the energy of the sound into thermal energy due to deformation of the dampening material. Vibration dampening materials are typically applied directly to the surface of the solid material. Examples of vibration dampening materials include rubber, plastic, bituminous or loaded Ethylene Vinyl Acetate (EVA) materials and the like.
Most studies on elastic PCs have focused on identifying an absolute and/or partial phononic band gaps, controlling the direction of propagation of longitudinal and transverse vibrations and attenuating the phase-relationship between acoustic signals. Others considered the role rigid body rotation (a consequence of Mie scattering) plays in modifying the bulk modes of propagation in the phononic structure. Rotary resonance modes can strongly interact with Bragg gaps to yield extremely wide absolute acoustic band gaps. A one-dimensional (1D), lumped model composed of finite-sized masses and mass-less springs can be further used to provide an understanding of the underlying physics behind rotary resonance in two-dimensional (2D), solid/solid PCs.
The continuum theory of elasticity was established by the Cosserat brothers, which accounted for the rotational degrees of freedom of individual elements in addition to the standard translational degrees of freedom used in classical elasticity theory. In the Cosserat model, each material element has six degrees of freedom—three for translation (in the xyz directions) and three for rotation (pitch, yaw, and roll). The theory introduces a couple-stress tensor (a component arising from the coupling of rotational and shear waves) that fulfills the same role for torques as the stress tensor of classical elasticity plays for forces. In an embodiment, Cosserat continuum elasticity theory can be used to predict that rotational degrees of freedom (e.g. rotational wave modes) can strongly modify the dispersion of shear waves. Characterization exists of rotational elastic waves in three-dimensional (3D) granular PCs—structures comprised of pre-compressed, regular arrangements of spherical elastic particles. In these, the Hertz-Mindlin contact model can be used to represent the connection between the elements of the PC.
In a related aspect, the body structures of vehicles are being engineered with increased stiffness in order to improve vehicle handling and the ability to withstand impact. As the stiffness of a vehicle body structure increases so too does the transmission of noise and vibration through the body structure. In order to minimize the transmission of vibration, sheets of vibration dampening material and/or sound dampening materials are typically placed in areas where vibrations and noise are most prevalent and likely to impact performance of the vehicle's components and their interaction with passengers. This approach has met with limited success and noise management remains an ever growing problem.
Thus, there remains a need for an improved sound and vibration dampening and attenuating materials that would be compatible increasing stiffness requirement associated with modern vehicles for example.